Geodesic
Hausdorff Operators on $p$-Adic Linear Spaces and Their Properties in Hardy, $BMO$, and H\"older Spaces
Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 357-367

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Sufficient conditions for the boundedness of $p$-adic matrix operators in Hardy, Hölder and $BMO$ spaces are obtained. These conditions are expressed in terms of the determinant of the matrix and its norm in a $p$-adic linear space.
Keywords: Hausdorff operator, $p$-adic linear space, Hardy space, Hölder space, the space $BMO$, $p$-adic matrix operator, Haar measure. 
@article{MZM_2013_93_3_a3,
     author = {S. S. Volosivets},
     title = {Hausdorff {Operators} on $p${-Adic} {Linear} {Spaces} and {Their} {Properties} in {Hardy,} $BMO$, and {H\"older} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {357--367},
     publisher = {mathdoc},
     volume = {93},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a3/}
}
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S. S. Volosivets. Hausdorff Operators on $p$-Adic Linear Spaces and Their Properties in Hardy, $BMO$, and H\"older Spaces. Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 357-367. http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a3/